An exact approach for single machine scheduling with quadratic earliness and tardiness penalties

her early schooling and unviersity preparatory studies in Qaemshahr. She then enrolled into Iran University of Science and Technology in Tehran after a highly selective admission procedure. In 2005, she finished her undergraduation studies in Mathematics with specialisation in topics of Applied Mathematics. After a brief 3-month training period spent working on updating flight managemeny system as a programmer, in 2009, she enrolled for master degree in Quentitative Methods in Economics and Management at the Faculty of Economics of University of Porto, and completed the course-work requirements in March 2011 with an average of 16.1/20. ii Acknowledgments I must thank many people for supporting me in my decision and in my efforts to pursue this Master degree. Apart from those that I mention here, the faculty of my course has been entirely understanding and supportive of my desire to pursue postgraduation in my tough times away from home. Special thanks to the director Professor Paulo Teles for the flexibility offered in following course-work. I am deeply grateful to the huge understanding support and guidance given by my supervisor Professor Jorge Valenet from whose academic experience i have benefited immensely. His gentle patience and precious words of motivation has helped me a lot in not only finishing this period well but also in thinking further about my future academic options. I am very thankful to my parents and my sister who have been a constant source of support, throughout my education. I am also glad to have had nice classmates and friends who made my stay smooth. And last but not the least, I am most fondly grateful to my husband Abolfazl without whose persuasion and unyielding patience this entire pursuit would not have been possible. iii Abstract In this study, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose two different lower bounds, as well as four lower bounding procedures. Five optimal branch-and-bound algorithms are then presented. Four algorithms incorporate the proposed lower bounding procedures, as well as an insertion-based dominance test, while the other one does not apply any lower bounding procedure. The lower bounding procedures and the branch-and-bound algorithms are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs.